What mass of a solution with a mass fraction of potassium hydroxide of 20% should be added to 1 kg

What mass of a solution with a mass fraction of potassium hydroxide of 20% should be added to 1 kg of a solution with a mass fraction of KOH 50% to obtain a solution with a mass fraction of KOH 25%?

1. Let’s designate: x – mass of solution with mass fraction of potassium hydroxide 20%. This means that there is 0.2 * x kilogram of pure potassium hydroxide.
2. If in a solution weighing 1 kilogram the mass fraction of potassium hydroxide is 50%, then the mass of pure potassium hydroxide is 1 * 0.5 = 0.5 kilograms
3. The mass of the total solution is 1 + x kilogram. The mass fraction of potassium hydroxide in it is 25%. Therefore, the mass of pure potassium hydroxide is 0.25 * (1 + x) kilogram.
4. Let’s make an equation based on the mass of pure potassium hydroxide:
0.2x + 0.5 = 0.25 * (1 + x);
0.2x + 0.5 = 0.25 + 0.25x;
0.25x – 0.2x = 0.5 – 0.25;
0.05x = 0.25;
x = 0.25 / 0.05;
x = 5;
Answer: you need 5 kilograms of a solution with a mass fraction of potassium hydroxide of 20%.